# Irreducible polynomial proof

Prove that X^n-1+X^n-2+........+X+1 is irreducible over Z iff n is prime.

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Prove that is irreducible over Z iff n is prime.

Proof:

Let

For n=2, we have f(x)=x+1, clearly is irreducible.

Now we suppose n>2. Since n given as prime, n must be odd ...

#### Solution Summary

This provides an example of proving a polynomial is irreducible.

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